Namespaces
Variants
Actions

Difference between revisions of "Pointed object"

From Encyclopedia of Mathematics
Jump to: navigation, search
m (better)
m (link)
Line 1: Line 1:
 
''of a category $\mathcal{C}$ having a terminal object''
 
''of a category $\mathcal{C}$ having a terminal object''
  
A pair $(X,x_0)$ where $X \in \mathrm{Ob}\,\mathcal{C}$ and $x_0$ is a morphism of the terminal object into $X$. An example is a pointed topological space (see [[Pointed space]]). The pointed objects of $\mathcal{C}$ form a category, in which the morphisms are the mappings sending the distinguished point to the distinguished point.
+
A pair $(X,x_0)$ where $X \in \mathrm{Ob}\,\mathcal{C}$ and $x_0$ is a morphism of the [[terminal object]] into $X$. An example is a pointed topological space (see [[Pointed space]]). The pointed objects of $\mathcal{C}$ form a category, in which the morphisms are the mappings sending the distinguished point to the distinguished point.
  
  

Revision as of 22:12, 2 November 2014

of a category $\mathcal{C}$ having a terminal object

A pair $(X,x_0)$ where $X \in \mathrm{Ob}\,\mathcal{C}$ and $x_0$ is a morphism of the terminal object into $X$. An example is a pointed topological space (see Pointed space). The pointed objects of $\mathcal{C}$ form a category, in which the morphisms are the mappings sending the distinguished point to the distinguished point.


Comments

The category of pointed objects of $\mathcal{C}$ has a zero object (see Null object of a category), namely the terminal object of $\mathcal{C}$ equipped with its unique point. Conversely, if a category $\mathcal{C}$ has a zero object, then it is isomorphic to its own category of pointed objects.

How to Cite This Entry:
Pointed object. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pointed_object&oldid=34261
This article was adapted from an original article by A.F. Kharshiladze (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article